Surface Acoustic Waves In Crystals Research Articles

Strong diffraction of nonlinear surface acoustic waves in crystals

Nonlinear distortion and shock formation in planar surface acoustic waves in anisotropic crystals have been modeled without [Hamilton et al., JASA (1999)] and with [Cormack et al., JASA 2022] piezoelectricity. Weak diffraction has been included in the paraxial approximation for nonlinear surface wave beams in isotropic solids [Shull et al., JASA (1995)]. Here, a procedure for including strong diffraction, i.e., without the paraxial approximation, in the model for nonlinear surface waves in crystals is presented, which incorporates the angular spectrum approach described by Kharusi and Farnell (JASA 1970). Anisotropy is defined by expressing the phase speed of a plane wave, and therefore, the magnitude of the corresponding wavenumber, as a function of the direction of propagation. Next, an explicit expression relating the two wavenumber components in the planar surface along which the wave propagates must be obtained as a function of direction, requiring iterative solution of a transcendental relation. The beam is then propagated incrementally away from the source, advancing the angular spectrum in k-space and including nonlinear interactions in the spatial domain to characterize the combined effects of diffraction and nonlinearity. Preliminary results are presented for converging nonlinear surface waves in crystals. [Work supported by IR&D at ARL:UT.]

Nonlinear piezoelectric surface acoustic waves.

The theory for nonlinear surface acoustic waves in crystals developed using Hamiltonian mechanics [Hamilton, Il'inskii, and Zabolotskaya, J. Acoust. Soc. Am. 105, 639 (1999)] is modified to account for piezoelectric material properties. The derived spectral evolution equations permit analysis of nonlinear surface wave propagation along a cut surface of any orientation with respect to the crystallographic axes and for piezoelectric crystals with any symmetry. Numerical simulations of waveform distortion in the particle velocity and electric field components are presented for surface wave propagation in Y-cut lithium niobate along the X- and Z-crystallographic axes. The influence of piezoelectricity is illustrated by comparing the nonlinear evolution of waveforms along a surface bounded by a vacuum (free space) and an ideal conductor (short circuit). Contributions to the nonlinearity from elasticity, piezoelectricity, electrostriction, and dielectricity are quantified separately for the two boundary conditions.

Holographic measurement of surface acoustic wave parameters in crystals

The theoretical basis of a specialized technique for applying digital holographic interferometry to measure the parameters of surface acoustic waves is presented, a measuring system for visualization and quantitative analysis of the parameters of ultralow-amplitude high-frequency oscillations arising in electronic devices using surface acoustic waves is developed, and experimental results of the study of surface acoustic waves in crystals of lithium niobate are obtained. In this case, to ensure the possibility of recording precision double-exposure interferograms of high-frequency surface acoustic waves, a picosecond pulsed laser with two-stage frequency multiplication was used as a radiation source, and to increase the spatial resolution of the system with the possibility of observing a wide field of view, an adjustable optical zoom of the incoming image was applied to the matrix input (based on charge-coupled devices) of the recording camera and digital zoom was used for obtained interferogram. We achieved the measuring sensitivity of the surface acoustic waves amplitude and spatial-temporal resolution allowing visualization and measurement of surface acoustic waves with amplitudes of the order of 1 nm and frequencies of the order of 10 MHz, which is far beyond the capabilities of standard methods of holographic interferometry.

Diffraction Distortion of Surface Acoustic Waves in Crystals

A method for the numerical modeling and visualization of the diffraction of surface acoustic waves propagating in anisotropic crystals is described. Examples of two-dimensional wave energy distributions are presented for some crystal orientations widely used in acoustoelectronics.

Comparative analysis of the search procedures for surface acoustic wave solutions in piezoelectric crystals

Various search procedures for finding the global extremum of a multivariate target function (TF) necessary for calculating the characteristics of surface acoustic waves (SAW) and leaky surface acoustic waves (LSAW) in crystals are analyzed. The search procedures aimed at determining the optimal orientations for SAW in crystals are considered. A comparative analysis of the promising methods for finding the global extremum of the TF is performed.

Calculation of Surface Acoustic Waves in Crystals Using the Global Optimization Procedure

The characteristics of surface acoustic waves are calculated using the procedure of searching for the global extremum of a multivariable function. This procedure is used to minimize the determinant of the boundary conditions to seek orientations in piezocrystals that are optimal from the viewpoint of acoustic-wave characteristics and to find pseudosurface (leaky) acoustic waves existing only in the vicinity of specific orientations.

Nonlinear surface acoustic waves in crystals

A theory for nonlinear surface acoustic waves in isotropic solids [E. A. Zabolotskaya, J. Acoust. Soc. Am. 91, 2569–2575 (1992)] is generalized to include the anisotropy of crystals. There is no restriction to material symmetry, orientation of the free surface with respect to crystal axes, or propagation direction in the plane of the free surface. Numerical simulations of waveform distortion, shock formation, and harmonic propagation curves are presented for two different cuts of potassium chloride.

Pulsed nonlinear surface acoustic waves in crystals

A theoretical model developed recently for the propagation of nonlinear surface acoustic waves in crystals [Hamilton et al., Nonlinear Acoustics in Perspective, edited by R. J. Wei (Nanjing U.P., Nanjing, 1996), pp. 64–69] is used to investigate transient effects associated with pulses. The present work extends an earlier theoretical investigation of pulsed nonlinear Rayleigh waves in isotropic solids [Knight et al., J. Acoust. Soc. Am. 96, 3322(A) (1994)]. The latter was verified via comparison with measurements of laser-generated nonlinear Rayleigh waves with shocks in fused quartz [Lomonosov et al., J. Acoust. Soc. Am. 101, 3080(A) (1997)]. Here simulations of waveform distortion and shock formation are presented for pulses in real crystals, including Si, KCl, and Ni, and for a variety of surface cuts and propagation directions. The second- and third-order elastic moduli in the nonlinearity matrix are taken from measurements reported in the literature. Attention is focused on waveforms corresponding to recent measurements of laser-generated nonlinear surface waves propagating in Si along the 〈112〉 direction in the (111) plane [Lomonosov and Hess, Nonlinear Acoustics in Perspective (Nanjing U.P., Nanjing, 1996), pp. 106–111]. Preliminary comparisons of theory with measurements obtained in related experiments are in good agreement. [Work supported by ONR and the RFBR Foundation.]